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Nonlinear BEM/FEM scalar potential formulation for magnetostatic analysis in superconducting accelerator magnets. (English) Zbl 1464.78022

Summary: Hybrid schemes that combine the Finite Element Method (FEM) and the Boundary Element Method (BEM) have been extensively used for the solution of nonlinear magnetostatic problems. The majority of those schemes rely either on reduced and total scalar or vector potential formulations. One main issue regarding the scalar potential formulations is the cancelation errors and difficulties on the definition of potential jump condition on the surface of a magnet, while in the case of vector potential formulations, the size of the simulated problem increases drastically especially in three dimensions. An alternative formulation has been proposed by I. D. Mayergoyz et al. [“A new scalar potential formulation for three-dimensional magnetostatic problems”, IEEE Trans. Magn. 23, No. 6, 3889–3894 (1987; doi:10.1109/TMAG.1987.1065774)], which is based on scalar potentials and provides assistance in ameliorating the aforementioned problems. In the present work that formulation is implemented by employing a BEM/FEM scheme, for the solution of nonlinear magnetostatic problems. The proposed BEM/FEM formulation is employed for the solution of representative magnetostatic problems dealing with different types of superconducting accelerator magnets, while the provided accuracy is assessed through comparisons made with corresponding results obtained by a well-known commercial FEM package.

MSC:

78M15 Boundary element methods applied to problems in optics and electromagnetic theory
65N38 Boundary element methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A30 Electro- and magnetostatics

Software:

APDL; ANSYS
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References:

[1] Wang, Q., Practical design of magnetostatic structure using numerical simulations (2013), John Wiley & Sons: John Wiley & Sons Singapore
[2] Magele, C.; Stogner, H.; Preis, K., Comparison of different finite element formulations for 3D magnetostatic problems, IEEE Trans Magn, 24, 31-34 (1988)
[3] Biro, O.; Preis, K.; Richter, K. R., On the use of the magnetic vector potential in the nodal and edge finite element analysis of 3D magnetostatic problems, IEEE Trans Magn, 32, 651-653 (1996)
[4] Alotto, P.; Perugia, I., A field-based finite element method for magnetostatics derived from an error minimization approach, Int J Numer Methods Eng, 49, 573-598 (2000) · Zbl 1028.78518
[5] Caciagli, A.; Baars, R. J.; Philipse, A. P.; Kuipers, B. W.M., Exact expression for the magnetic field of a finite cylinder with arbitrary uniform magnetization, J Magn Magn Mater, 456, 423-443 (2018)
[6] Bruckner, F.; d’Aquino, M.; Serpico, C.; Abert, C.; Vogler, C.; Suess, D., Large scale finite-element simulation of micromagnetic thermal noise, J Magn Magn Mater, 475, 408-414 (2019)
[7] Rucker, W. M.; Richter, K. R., Three-dimensional magnetostatic field calculation using boundary element method, IEEE Trans Magn, 24, 23-26 (1988)
[8] Roeckelein, R.; v.d. Berg, H. A.M., Modelling of permanent magnets with the boundary element method, Eng Anal Bound Elem, 7, 3, 119-123 (1990)
[9] Krstajic, B.; Andjelic, Z.; Miloijkovic, S.; Babic, S., Nonlinear 3D magnetostatic field computation by the integral equation method with surface and volume magnetic charges, IEEE Trans Magn, 28, 1088-1091 (1992)
[10] Rucker, W. M.; Magele, Ch.; Schlemmer, E.; Richter, K. R., Boundary element analysis of 3-D magnetostatic problems using scalar potentials, IEEE Trans Magn, 28, 1099-1102 (1992)
[11] Kurgan, E., A boundary element solution of the inhomogeneous magnetostatic problems, Appl Numer Math, 28, 343-358 (1998) · Zbl 0924.65114
[12] Kim, D.; Park, I.; Park, M.; Lee, H., 3-D magnetostatic field calculation by a single layer boundary integral equation method using a difference field concept, IEEE Trans Magn, 36, 5, 3134-3136 (2000)
[13] Fanga, Z.; Ingber, M. S.; Martinez, M. J., The solution of magnetostatic BEM systems of equations using iterative methods, Eng Anal Bound Elem, 26, 789-794 (2000) · Zbl 1033.78013
[14] Lobry, J., A new BEM technique for nonlinear 2D magnetostatics, Eng Anal Bound Elem, 26, 795-801 (2002) · Zbl 1033.78014
[15] Buchau, A.; Rucker, W. M.; Rain, O.; Rischmüller, V.; Kurz, S.; Rjasanow, S., Comparison between different approaches for fast and efficient 3D BEM computations, IEEE Trans Magn, 39, 1107-1110 (2003)
[16] Hafla, W.; Buchau, A.; Rucker, W. M., Accuracy improvement in nonlinear magnetostatic field computations with integral equation methods and indirect total scalar potential formulations, COMPEL: Int J Comput Math Electr Electron Eng, 25, 3, 565-571 (2006) · Zbl 1124.78317
[17] Andjelic, Z.; Of, G.; Steinbach, O.; Urthaler, P., Boundary element methods for magnetostatic field problems: a critical view, Comput Vis Sci, 14, 117-130 (2011) · Zbl 1243.78047
[18] Ingber, M. S.; Kiuttu, G. F., An ancillary boundary integral equation for magnetostatic analysis, Eng Anal Bound Elem, 36, 77-80 (2012) · Zbl 1245.78014
[19] Moro, F.; Codecasa, L., Indirect coupling of the cell method and BEM for solving 3-D unbounded magnetostatic problems, IEEE Trans Magn, 52, 3, Article 7200604 pp. (2016)
[20] Chang, J. H.; Becker, E. B.; Driga, M. D., On the calculation of coaxial electromagnetic launcher with FE-BE method, Eng Anal Bound Elem, 11, 119-128 (1993)
[21] Balac, S.; Caloz, G., Magnetostatic field computations based on the coupling of finite element and integral representation methods, IEEE Trans Magn, 38, 2, 393-396 (2002)
[22] Frangi, A.; Faure-Ragani, P.; Ghezzi, L., Magneto-mechanical simulations by a coupled fast multipole method-finite element method and multigrid solvers, Comput Struct, 83, 10, 718-726 (2005)
[23] Frangi, A.; Ghezzi, L.; Faure-Ragani, P., Accurate force evaluation for industrial magnetostatics applications with fast BEM-FEM approaches, CMES: Comput Methods Eng Sci, 15, 1, 41-48 (2006) · Zbl 1357.78006
[24] Salgado, P.; Selgas, V., A symmetric BEM-FEM coupling for the three-dimensional magnetostatic problem using scalar potentials, Eng Anal Bound Elem, 32, 8, 633-644 (2008) · Zbl 1244.78030
[25] Pusch, D.; Ostrowski, J., Robust FEM/BEM coupling for magnetostatics on multiconnected domains, IEEE Trans Magn, 46, 8, 3177-3180 (2010)
[26] Lukás, D.; Postava, K.; Zivotsky, O., A shape optimization method for nonlinear axisymmetric magnetostatics using a coupling of finite and boundary elements, Math Comput Simul, 82, 1721-1731 (2012) · Zbl 1253.78053
[27] Bruckner, F.; Vogler, C.; Feischl, M.; Praetorius, D.; Bergmair; Huber, T.; Fuger, M.; Suess, D., 3D FEM-BEM-coupling method to solve magnetostatic Maxwell equations, J Magn Magn Mater, 324, 1862-1866 (2012)
[28] May, S.; Kästner, M.; Müller, S.; Ulbricht, V., A hybrid IGAFEM/IGABEM formulation for two-dimensional stationary magnetic and magneto-mechanical field problems, Comput Methods Appl Mech Eng, 273, 161-180 (2014) · Zbl 1296.74122
[29] Araujo, D. M.; Meunier, G.; Chadebec, O.; Coulomb, J. L.; Rondot, L., 3-D Hybrid FEM-BEM using Whitney facet elements and independent loops, IEEE Trans Magn, 51, 3, 1-4 (2015)
[30] Hertel, R.; Kákay, A., Hybrid finite-element/boundary-element method to calculate Oersted fields, J Magn Magn Mater, 369, 189-196 (2014)
[31] Hertel, R.; Christophersen, S.; Börm, S., Large-scale magnetostatic field calculation in finite element micromagnetics with H2-matrices, J Magn Magn Mater, 477, 118-123 (2019)
[32] Sykulski, J. K., Computational magnetics (1995), Chapman & Hall
[33] Russenschuck, S., Field computation for accelerator magnets (2010), Wiley-VCH · Zbl 1229.78001
[34] Bastos, J. P.A.; Sadowski, N., Magnetic materials and 3D finite element modeling (2014), CRC Press
[35] Mayergoyz, I. D.; Chari, M. V.K.; D’Angelo, J., A new scalar potential formulation for three-dimensional magnetostatic problems, IEEE Trans Magn, 23, 3889-3894 (1987)
[36] Rodopoulos, D. C.; Gortsas, T. V.; Polyzos, K.; Tsinopoulos, S. V., New BEM/BEM and BEM/FEM scalar potential formulations for magnetostatic problems, Eng Anal Bound Elem, 106, 160-169 (2019) · Zbl 1464.78021
[37] Stratton, J. A., Electromagnetic theory (1941), McGraw-Hill: McGraw-Hill New York, NY · JFM 67.1119.01
[38] Tsinopoulos, S. V.; Kattis, E.; Polyzos, D., Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies, Comput Mech, 21, 306-315 (1998) · Zbl 0915.65127
[39] Wrobel, L. C., The boundary element method. volume1: applications in thermo-fluids and acoustics (2002), Wiley: Wiley England
[40] Kokkinos, C.; Karppinen, M., High gradient Nb_3Sn quadrupole demonstrator MKQXF engineering design, (Proceedings of the 2017 magnet technology 25-006(B) (2017))
[41] Marinozzi, V.; Bellomo, G.; Caiffi, B.; Fabbricatore, P.; Farinon, S.; Ricci, A. M.; Sorbi, M.; Statera, M., Conceptual design of a 16 T cosθ bending dipole for the future circular collider, IEEE Trans Appl Superconduct, 28, 3, 4004205 (2018)
[42] Caiffi, B.; Bellomo, G.; Fabbricatore, P.; Farinon, S.; Marinozzi, V.; Ricci, A. M.; Sorbi, M., Update on mechanical design of a cosθ 16-T bending dipole for the future circular collider, IEEE Trans Appl Superconduct, 28, 4, 4006704 (June 2018)
[43] ANSYS® Mechanical APDL Theory Reference, Release 15.0, (2013), ANSYS, Inc.
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